0625 · 3.2Light

Reflection and plane mirrors

0:00A mirror makes an object appear behind a surface that light cannot pass through. A magnifying glass makes small writing look larger. A glass prism separates white light into colours. These effects seem different, but they follow a few connected rules. In this video, we will follow light rays to understand images, refraction, lenses and colour. We need two starting ideas. In a uniform transparent material, light travels in straight lines.

0:24A ray represents the direction in which light travels, and its arrow shows that direction. We see an object when light from it enters our eyes. An image forms where those rays meet, or where they appear to come from. Begin with reflection, where light returns into the medium it came from. At the point where a ray strikes a surface, draw the normal. The normal is an imaginary line perpendicular to the surface.

0:48Perpendicular means at ninety degrees to it. This line gives us a consistent reference for measuring the direction of each ray. The angle of incidence is the angle between the incident ray and the normal. The angle of reflection is the angle between the reflected ray and the normal. For reflection, the angle of incidence equals the angle of reflection. Both angles are measured from the normal, not from the mirror surface.

1:10That distinction matters whenever you draw or calculate a reflected path. Here is a worked reflection calculation, using an Extended construction skill. A ray makes an angle of thirty degrees with a plane mirror surface. The angle of incidence is ninety degrees minus thirty degrees, giving sixty degrees. The angle of reflection therefore equals sixty degrees. The reflected ray makes thirty degrees with the surface on the other side of the normal.

1:35For an accurate construction, use a ruler to draw the mirror and incident ray. Draw the normal at the point of incidence. Measure the incidence angle using a protractor, then mark an equal reflection angle on the opposite side. Draw the reflected ray through that mark and add an arrow pointing away from the mirror. The diagram now represents the law of reflection. Now follow two rays from one point on an object.

1:58After reflection, they enter your eye, but they do not meet behind the mirror. Your brain interprets arriving light as travelling along straight paths. Extend the reflected rays backwards using dashed lines. Their extensions meet behind the mirror, showing where the light appears to have originated. A plane mirror forms an image that is upright and the same size as the object. The image is as far behind the mirror as the object is in front.

2:21It is virtual because the light rays only appear to meet there. A virtual image cannot be formed as a visible projection on a screen. No light actually travels through that apparent image position. You can also locate the image using an Extended geometrical construction. Draw a perpendicular from the object to the mirror, then continue it behind the mirror. Mark the image at an equal perpendicular distance behind. For an object twelve centimetres in front, the image is twelve centimetres behind.

2:47The distance between object and image is therefore twenty-four centimetres.

Refraction through transparent blocks

2:52Reflection sends light back, but transparent materials can also transmit it. Refraction is the change in direction of light when it passes between media because its speed changes. A medium is a material or region through which light travels. The angle of refraction is the angle between the refracted ray and the normal. Again, measure from the normal rather than the boundary. Light travels more slowly in glass than in air.

3:17Entering glass at an angle, it bends towards the normal. Leaving glass for air, it speeds up and bends away from the normal. Along the normal, its speed changes but its direction does not. Refraction does not mean that every ray crossing a boundary must bend. A useful comparison is a line of people entering deep sand at an angle. One end slows before the other, so the line changes direction.

3:40Light is a wave, and its change of speed similarly changes its direction at an angled boundary. Its frequency stays unchanged when it enters another medium. Its wavelength changes because its speed changes. To investigate refraction, place a rectangular transparent block on paper and trace its outline. Direct a narrow ray from a ray box obliquely at one face. Mark points along the incoming and outgoing paths, keeping your eyes away from the beam.

4:04Remove the block and join the marks with a ruler. Join the entry and exit points to show the path inside. Draw normals at both boundaries and measure the angles with a protractor. The ray bends towards the normal on entering glass and away on leaving. For a rectangular block surrounded by air, the emerging ray is parallel to the incident ray. It is displaced sideways because it travelled diagonally through the block.

4:27Repeat with different incidence angles to compare the paths. Repeat the investigation with a triangular block and a semicircular block. Trace each outline and mark the rays before removing the block. A prism has non-parallel faces, so its emerging ray is generally not parallel to the incident ray. With a semicircular block, aim the ray at the centre of the flat side. The ray then crosses the curved side along a normal, so it does not bend there.

4:53Any bending you see happens at the flat side.

Refractive index and total internal reflection

4:55Now we reach the Extended treatment of refractive index. Refractive index is the ratio of the speeds of a wave in two different regions. For light entering glass from air, divide its speed in air by its speed in glass. A larger refractive index means a greater reduction in speed. Because it compares two speeds, refractive index has no unit. For example, light travels at approximately three hundred million metres per second in air.

5:21Suppose it travels at two hundred million metres per second in a transparent material. Its refractive index is three hundred million divided by two hundred million. The result is one point five, with no unit. This tells us the speed in air is one point five times the speed inside. For light entering a material from air, refractive index equals sine of the angle of incidence divided by sine of the angle of refraction.

5:44This relationship connects the speed change with the change in direction. Sine is a calculator function applied to each angle. Use degree mode for these calculations. Do not divide the angles themselves, because the relationship uses their sines. Suppose the angle of incidence is forty degrees and the angle of refraction is twenty-five degrees. First, take the sine of forty degrees, giving approximately zero point six four three. Next, take the sine of twenty-five degrees, giving approximately zero point four two three.

6:14Divide the first result by the second to obtain approximately one point five two. That is the refractive index. The smaller refraction angle is consistent with light slowing down and bending towards the normal. You can also rearrange the relationship to find an unknown angle. Sine of the refraction angle equals sine of the incidence angle divided by refractive index. Then use inverse sine to obtain the angle. Always check that your answer matches the expected bending direction.

6:40Now send light from glass towards air. Some light can reflect internally while some leaves by refraction. As the angle of incidence increases, the refracted ray moves closer to the boundary. The critical angle is the angle of incidence for which the angle of refraction is ninety degrees. At this angle, the refracted ray travels along the boundary. Above the critical angle, no refracted ray passes into the air, and all the light is reflected back into the glass.

7:07This is total internal reflection. It needs two conditions. Light must travel towards a medium with a lower refractive index, and its angle of incidence must exceed the critical angle. Ordinary internal reflection can occur without satisfying both conditions, but total internal reflection cannot. You can demonstrate this with the semicircular block. Aim the ray through the centre of curvature so it enters without bending at the curved surface. Increase its angle of incidence at the flat glass-to-air boundary.

7:35Observe refraction below the critical angle and a grazing refracted ray at the critical angle. Above it, observe only the internally reflected ray. The next calculation is Extended content. At the critical angle, the refraction angle is ninety degrees, whose sine equals one. Applying the refraction relationship in reverse gives refractive index equals one divided by sine of the critical angle. This equation applies to the material-to-air boundary considered here.

8:01It connects the critical angle to how strongly the material slows light. For glass with refractive index one point five, sine of the critical angle equals 1 ÷ 1.5. That gives approximately zero point six six seven. Taking inverse sine gives a critical angle of approximately forty-one point eight degrees. An internal incidence angle of fifty degrees is greater than this. Therefore, light travelling from this glass towards air undergoes total internal reflection.

8:28Optical fibres are an Extended application of total internal reflection. A fibre has a transparent core surrounded by cladding with a lower refractive index. Light meeting this boundary above the critical angle reflects back into the core. Repeated reflections guide light along the fibre. In telecommunications, pulses of light carry information between places. A fibre can guide light around gentle curves while the conditions for total internal reflection remain satisfied.

8:56Very sharp bends can allow light to escape. Medical viewing instruments provide another familiar use of optical fibres. A prism can also redirect light by total internal reflection, as in some binoculars. These applications use reflection inside transparent material rather than a silvered mirror.

Lenses, images and eyesight

9:12Lenses use refraction at curved boundaries to control whole beams of light. A thin converging lens brings rays parallel to its principal axis together at the principal focus. The principal axis is the straight line through the optical centre, perpendicular to the lens. The focal length is the distance from the optical centre to the principal focus. A converging lens is thicker at its centre. A thin diverging lens is thinner at its centre and spreads a parallel beam apart.

9:39Its principal focus is where those diverging rays appear to originate. Find it by extending the outgoing rays backwards. The focal length is measured between that focus and the optical centre. Light can enter from either side, so lenses have a principal focus on each side. To construct a converging-lens image, draw the principal axis, lens and both principal foci. Draw an upright object arrow with its base on the axis.

10:04From its top, draw a ray parallel to the axis, then through the far focus. Draw another ray through the optical centre, continuing straight for a thin lens. Their intersection locates the top of the image. Here, the refracted rays actually meet, producing a real image. A screen placed at that position receives a visible projection. Because rays from the object’s top meet below the axis, the image is inverted.

10:28Its size depends on the object position. An image is real because the rays actually meet there. Being upside down is not what makes it real. Beyond twice the focal length, an object produces a diminished image between one and two focal lengths on the opposite side. At twice the focal length, its image is the same size. Between one and two focal lengths, the image is enlarged and forms beyond twice the focal length.

10:51All these images are real and inverted. At the focus, the emerging rays are parallel. Virtual-image construction with a converging lens is Extended content. Place the object between the lens and its near principal focus. Draw the same two rays from the object’s top. After refraction, they diverge rather than meet. Extend them backwards with dashed lines to locate the virtual image on the object’s side of the lens. That image is upright and enlarged, which explains a magnifying glass.

11:18Hold a converging lens with the object closer than one focal length. Your eye receives diverging rays that appear to come from a larger object. The virtual image cannot be projected onto a screen. Describing an image means stating its size, orientation and whether it is real or virtual. Correcting eyesight is also Extended content. In short-sightedness, light from a distant object would focus in front of the retina. The retina is the light-sensitive surface at the back of the eye.

11:46A diverging lens spreads incoming rays before they enter the eye. The eye then focuses them on the retina instead of in front of it. In long-sightedness, light from a nearby object would focus behind the retina. A converging spectacle lens starts bringing those rays together before they enter the eye. The combined effect moves the focus onto the retina. Keep the correction linked to the direction of the error.

12:09Diverging lenses correct short-sightedness, while converging lenses correct long-sightedness.

Dispersion and the visible spectrum

12:13Finally, a glass prism reveals that white light contains different colours. Dispersion is the separation of white light into its constituent colours. Different colours travel at slightly different speeds in glass, so they refract by different amounts. Red light is deviated least and violet most in an ordinary glass prism. The prism separates existing colours rather than creating them. The traditional seven colours are red, orange, yellow, green, blue, indigo and violet.

12:41In that order, frequency increases and wavelength decreases. For increasing wavelength, reverse the order from violet to red. The spectrum is continuous rather than seven sharply separated bands. The seven names describe familiar regions within that continuous range of visible colours. For Extended students, visible light of a single frequency is described as monochromatic. White light is not monochromatic because it contains a range of frequencies. Refraction changes a colour’s speed and wavelength in glass, but not its frequency.

13:12This explains how colours can bend differently without becoming different colours. Remember that violet has higher frequency and shorter wavelength than red.

Exam answers and recap

13:20An exam-style question asks you to explain total internal reflection in glass of refractive index one point five at fifty degrees. A precise answer says that light is travelling from glass towards air, which has a lower refractive index. The critical angle is approximately forty-two degrees. The angle of incidence exceeds the critical angle. Therefore, all the light is reflected internally, with no refracted ray entering the air. Watch for three connected mistakes.

13:47Measuring from the surface gives the wrong angle because the equations use angles measured from the normal. Treating dashed image rays as actual light paths confuses a virtual image with a real one. Claiming that every glass-to-air ray undergoes total internal reflection ignores the critical angle. In each case, the diagram should help you check the physical meaning. Let us bring everything together. Reflection returns light with equal incidence and reflection angles, while refraction changes its direction when its speed changes.

14:16Mirrors and lenses form images according to where rays meet or appear to originate. Total internal reflection guides light inside fibres when its conditions are satisfied. Dispersion separates white light because different colours refract by different amounts.